Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# The Value of Lim X → ∞ N ! ( N + 1 ) ! − N ! - Mathematics

MCQ

The value of $\lim_{x \to \infty} \frac{n!}{\left( n + 1 \right)! - n!}$

#### Options

•  1

•  −1

• none of these

#### Solution

$\lim_{n \to \infty} \frac{n!}{\left( n + 1 \right)! - n!}$
$\text{ Dividing } N^r \text{ and } D^r \text{ by } n!:$
$\lim_{n \to \infty} \frac{1}{\frac{\left( n + 1 \right)!}{n!} - 1}$
$= \lim_{n \to \infty} \frac{1}{\frac{\left( n + 1 \right)n!}{n!} - 1}$
$= \lim_{n \to \infty} \frac{1}{n + 1 - 1}$
$= \lim_{n \to \infty} = \frac{1}{n} = 0$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 29 Limits
Q 35 | Page 80